What is the limit as x approaches infinity of ((x+1)/(x-1))^{x-1} ?

The limit as x approaches infinity of ((x+1)/(x-1))^{x-1} is e^2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

limit as x approaches infinity of ((x+1)/(x-1))^{x-1}

x \to \infty lim ((\frac{x + 1}{x - 1})^{x - 1})

e^{2}

Decimal Notation

7.38905 \dots

Solution steps

x \to \infty lim ((\frac{x + 1}{x - 1})^{x - 1})

Simplify

(\frac{x + 1}{x - 1})^{x - 1} : (\frac{x + 1}{x - 1})^{x} (\frac{x + 1}{x - 1})^{- 1}

= x \to \infty lim ((\frac{x + 1}{x - 1})^{x} (\frac{x + 1}{x - 1})^{- 1})

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

With the exception of indeterminate form

= x \to \infty lim ((\frac{x + 1}{x - 1})^{x}) \cdot x \to \infty lim ((\frac{x + 1}{x - 1})^{- 1})

x \to \infty lim ((\frac{x + 1}{x - 1})^{x}) = e^{2}

x \to \infty lim ((\frac{x + 1}{x - 1})^{- 1}) = 1

= e^{2} \cdot 1

Simplify

= e^{2}

x \to 0 + lim (7 x ln (x))

x \to 0 + lim (e^{- \frac{1}{x}} \cdot x^{- 2})

x \to 0 lim (x^{2} sin (\frac{π}{x}))

x \to 3 lim (x - 7)

What is the limit as x approaches infinity of ((x+1)/(x-1))^{x-1} ?
The limit as x approaches infinity of ((x+1)/(x-1))^{x-1} is e^2